How do you find the equation of the tangent line to the graph of #f(x)=x^3+1# at point (1,2)?

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Answer 1 · 2017-09-01T14:06:06

The derivative of #f(x)# is given by the power rule, which states that #d/dx(x^n) = nx^(n -1)#. .

#f'(x) = 3x^(3 - 1) + 0(1)x^(0 - 1)#

#f'(x) = 3x^2#

We now determine the slope of the tangent line by plugging in the point #x =a# into the derivative.

#f'(1) = 3(1)^2 = 3#

Now we can readily find the equation of the line.

#y -y_1 = m(x - x_1)#

#y - 2 = 3(x - 1)#

#y = 3x - 3 + 2#

#y = 3x - 1#

Now we can check the graphical interpretation and confirm that we are correct.

Desmos

Hopefully this helps!